Learning context-free grammars using tabular representations

We present a novel algorithm using new hypothesis representations for learning context-free grammars from a finite set of positive and negative examples. We propose an efficient hypothesis representation method which consists of a table-like data structure similar to the parse table used in efficient parsing algorithms for context-free grammars such as Cocke-Younger-Kasami algorithm. By employing this representation method, the problem of learning context-free grammars from examples can be reduced to the problem of partitioning the set of nonterminals. We use genetic algorithms for solving this partitioning problem. Further, we incorporate partially structured examples to improve the efficiency of our learning algorithm, where a structured example is represented by a string with some parentheses inserted to indicate the shape of the derivation tree of the unknown grammar. We demonstrate some experimental results using these algorithms and theoretically analyse the completeness of the search space using the tabular method for context-free grammars.     

A CKY parser for picture grammars

We study the complexity of the membership or parsing problem for pictures generated by a family of picture grammars: Siromoney's Context-Free Kolam Array grammars (coincident with Matz's context-free picture grammars). We describe a new parsing algorithm, which extends the Cocke, Kasami and Younger's classical parsing technique for string languages and preserves the polynomial time complexity.     

The parsing problem for affix grammars

Summary Affix grammars are an extension of context-free grammars which retain most of their advantages and eliminate most of their limitations with respect to the definition of programming languages and the specification of their translators. The extension allows definition of context-sensitive syntax features, and also allows semantics to be linked to syntax. In this paper, the parsing problem for affix grammars is explored and shown to be closely related to the parsing problem for context-free grammars. This enables a standard context-free parser constructor to be generalised to a constructor for affix grammars, essentially by addition of a preprocessor. The resulting constructors are compared with previously implemented or proposed constructors.     

Dynamic LL(k) parsing

A new class of context-free grammars, called dynamic context-free grammars, is introduced. These grammars have the ability to change the set of production rules dynamically during the derivation of some terminal string. The notion of LL() parsing is adapted to this grammar model. We show that dynamic LL() parsers are as powerful as LR() parsers, i.e. that they are capable to analyze every deterministic context-free language while using only one symbol of lookahead. Received: 24 August 1994 / 5 January 1996     

A parsing methodology for the implementation of visual systems

The Visual Language Compiler-Compiler (VLCC) is a grammar-based graphical system for the automatic generation of visual programming environments. In this paper the theoretical and algorithmic issues of VLCC are discussed in detail. The parsing methodology we present is based on the “positional grammar” model. Positional grammars naturally extend context-free grammars by considering new relations in addition to string concatenation. Thanks to this, most of the results from LR parsing can be extended to the positional grammars inheriting the well known LR technique efficiency. In particular, we provide algorithms to implement a YACC-like tool embedded in the VLCC system for automatic compiler generation of visual languages described by positional grammars     

A class of linearly parsable graph grammars

Summary Specializing an existing graph grammar model we look in detail at node context-free graph grammars. With a slight generalization the parse trees for context-free Chomsky grammars can be used to describe derivations of these graph grammars.As shown already in former works the precedence graph grammars are defined as a subclass of context-free graph grammars by certain algebraic restrictions on the form of the rules. Then we can prove that every precedence grammar is unambiguous and additionally the reduction process in such a grammar read as replacement system is finite.The most important aim in defining the predence relations was a simple parsing method. This is realized because it is shown that the syntactic analysis for precedence graph grammars can be done in a time which linearly depends on the size of the input graph.The whole method has been implemented and a documentation is available.     

一种特殊的上下文无关文法及其语法分析

SAQ系统是一个进行软件规约获取、检验和复用的实验系统，其中以上下文无关文法表示的概念是规约的一部分.SAQ要求将概念的词法和句法定义结合在一个上下文无关文法中.如果用常规的上下文无关文法描述诸如程序设计语言和自然语言等一些复杂概念的语法，则需要把诸如空格和回车等没有实质意义的分隔符包含到语法中去(这种描述方法称为朴素表示法),使得语法描述很累赘.为此，作者设计了一种特殊的上下文无关文法,它把通常上下文无关文法定义中的非终极符集合和终极符集合进行细化.用这种文法可以相对简洁地描述程序语言和自然语言等复杂概     

Efficiently building a parse tree from a regular expression

We show in this paper that parsing with regular expressions instead of context-free grammars, when it is possible, is desirable. We present efficient algorithms for performing different tasks that concern parsing: producing the external representation and the internal representation of parse trees; producing all possible parse trees or a single one. Each of our algorithms to produce a parse tree from an input string has an optimal time complexity, linear with the length of the string. Moreover, ambiguous regular expressions can be used. Received: 21 October 1997 / 30 May 2000     

Context-free graph grammars and concatenation of graphs

An operation of concatenation is defined for graphs. This allows strings to be viewed as expressions denoting graphs, and string languages to be interpreted as graph languages. For a class of string languages, is the class of all graph languages that are interpretations of languages from . For the classes REG and LIN of regular and linear context-free languages, respectively, . is the smallest class of graph languages containing all singletons and closed under union, concatenation and star (of graph languages). equals the class of graph languages generated by linear HR (= Hyperedge Replacement) grammars, and is generated by the corresponding -controlled grammars. Two characterizations are given of the largest class such that . For the class CF of context-free languages, lies properly inbetween and the class of graph languages generated by HR grammars. The concatenation operation on graphs combines nicely with the sum operation on graphs. The class of context-free (or equational) graph languages, with respect to these two operations, is the class of graph languages generated by HR grammars. Received 16 October 1995 / 18 September 1996     

An LR parsing technique for extended context-free grammars

Extended context-free grammars allow regular expressions to appear in productions right hand sides, and are a clear and natural way to describe the syntax of programming languages.In this paper an LR parsing technique for extended context-free grammars is presented, which is based on an underlying transformation of the grammar into an equivalent context-free one.The technique is suitable for inclusion in one-pass compilers: the implementation requires little extensions to the algorithms working for normal LR grammars. Besides describing the parsing method, the paper shows also the algorithms for deriving the parsing tables; tables optimization is also discussed. Finally, this technique is compared with other proposals appeared in the literature.     

THE COMPUTATIONAL COMPLEXITY OF THE UNIVERSAL RECOGNITION PROBLEM FOR PARALLEL MULTIPLE CONTEXT-FREE GRAMMARS

A number of grammatical formalisms have been proposed to describe the syntax of natural languages, and the universal recognition problems for some of those classes of grammars have been studied. A universal recognition problem for a class Q of grammars is the one to decide, taking a grammar G ∈ G and a string ui as an input, whether G can generate w or not. In this paper, the computational complexities of the universal recognition problems for parallel multiple context-free grammars, multiple context-free grammars, and their subclasses are discussed.     

On the structure of node-label-controlled graph languages

A new kind of graph grammars (called NLC grammars) is introduced. The main theorem is a result on the combinatorial structure of graph languages generated by NLC grammars; it resembles the pumping theorem for context-free string languages.     

Fundamental methodological issues of syntactic pattern recognition

Fundamental open problems, which are frontiers of syntactic pattern recognition are discussed in the paper. Methodological considerations on crucial issues in areas of string and graph grammar-based syntactic methods are made. As a result, recommendations concerning an enhancement of context-free grammars as well as constructing parsable and inducible classes of graph grammars are formulated.     

Parsing of edNLC-graph grammars for scene analysis

An edNLC-graph grammar, introduced by Janssens,⁽⁴⁾ is a strong formalism for generating scene representations. This grammar generates directed node- and edge-labelled graphs, EDG-graphs. A method of construction of unambiguous string EDG-graph representation is briefly described. The characteristics of edNLC-graph grammar for syntactic pattern recognition allows us to construct the parsing algorithm. The deterministic top-down syntax analyzer is constructed for the subfamily of an edNLC-graph grammar, called an ETL/1-graph grammar. An ETL/1-graph grammar is parallel to a finite state string grammar. The notions introduced in the paper are useful for researches in less restricted edNLC-graph grammars, for example grammars analogical to context-free string grammars.     

Adaptive star grammars and their languages

Motivated by applications that require mechanisms for describing the structure of object-oriented programs, adaptive star grammars are introduced, and their fundamental properties are studied. In adaptive star grammars, rules are actually schemata which, via the cloning of so-called multiple nodes, may adapt to potentially infinitely many contexts when they are applied. This mechanism makes adaptive star grammars more powerful than context-free graph grammars. Nevertheless, they turn out to be restricted enough to share some of the basic characteristics of context-free devices. In particular, the underlying substitution operator enjoys associativity and confluence properties quite similar to those of context-free graph grammars, and the membership problem for adaptive star grammars is decidable.     

LL(k)-PARSING OF COUPLED-CONTEXT-FREE GRAMMARS

Coupled-context-free grammars are a natural generalization of context-free grammars obtained by combining nonterminals to corresponding parentheses which can only be substituted simultaneously. Refering to the generative capacity of the grammars we obtain an infinite hierarchy of languages that comprises the context-free languages as the first and all the languages generated by TAGs as the second element. Here, we present a generalization of the context-free LL(k) -notion onto coupled-context-free grammars, which leads to a characterization of subclasses of coupled-context-free grammars–and in this way of TAGs as well–which can be parsed in linear time. The parsing procedure described works incrementally so that it can be used for on-line parsing of natural language. Examples show that important elements of the tree-adjoining languages can be generated by LL(k )-coupled-context-free grammars.     

A non-left-to-right,non-directional parser for ambiguous lattices

In syntactic pattern recognition the need of reducing computational power may require the use of more general parsers than the standard ones, allowing to efficiently exploit the structural knowledge for limiting the extraction of primitive patterns. In this paper a new flexible, non-directional, non-left-to-right parsing scheme is presented; it has worst case space complexity O(N²) and time complexity O(N³), where N is the length of the input string. These upper bounds are lowered for particular classes of context-free grammars as, for instance, linear or non-ambiguous ones.     

Probabilistic context-free grammars estimated from infinite distributions

In this paper, we consider probabilistic context-free grammars, a class of generative devices that has been successfully exploited in several applications of syntactic pattern matching, especially in statistical natural language parsing. We investigate the problem of training probabilistic context-free grammars on the basis of distributions defined over an infinite set of trees or an infinite set of sentences by minimizing the cross-entropy. This problem has applications in cases of context-free approximation of distributions generated by more expressive statistical models. We show several interesting theoretical properties of probabilistic context-free grammars that are estimated in this way, including the previously unknown equivalence between the grammar cross-entropy with the input distribution and the so-called derivational entropy of the grammar itself. We discuss important consequences of these results involving the standard application of the maximum-likelihood estimator on finite tree and sentence samples, as well as other finite-state models such as hidden Markov models and probabilistic finite automata.     

Hierarchical structures and complexities of parallel isometric languages

The relationship between parallel isometric array languages and sequential isometric array languages is examined. Their hierarchical structures are investigated and a hierarchy is established by introducing parallel context-free array languages (PCFAL), derivation bounded array languages (DBAL), linear array languages (LAL), and extended regular afray languages (ERAL). It is interesting to find that some fundamental aspects that hold in one-dimensional string languages do not hold in their two-dimensional counterparts. Some parsing techniques are also explored. It is shown that while parallel parsing grammars may be simpler to write and parallel processing usually takes less time than sequential ones, the nature of parallel parsing is very complicated. Finally, several future research topics concerned with parallel isometric array languages including their complexities, hierarchical structures, and application to pattern recognition are discussed.